Doping and magnetic field dependence of in-plane tunneling into YBa(2)Cu(3)O(7-x): possible evidence for the existence of a quantum critical point.

We present tunneling measurements into (1,1,0) YBa(2)Cu(3)O(7-x) films at various doping levels around the optimum. We find that, above a certain doping level near optimum doping, a spontaneous zero bias conductance peak splitting, delta, appears. It increases with doping. It also increases with magnetic field applied along the c axis, for both underdoped and overdoped films. The low field susceptibility chi = d delta /dH/(H-->0) is maximum, possibly diverging when the spontaneous value of delta goes to zero. These results suggest a transition from a pure d(x(2)-y(2)) to a d+id(xy) or d+is order parameter.